Build, Check, Solve

Overview

In this second lesson of the Whole Number Operations unit, the student adds and subtracts multi-digit whole numbers by aligning place-value columns. The student then checks calculations with inverse operations and addition’s commutative property and solves an unknown-value equation.

Learning intentions

Students will be able to:

• Add and subtract multi-digit whole numbers using aligned place-value columns.
• Explain how regrouping reflects the value of each place.
• Use inverse operations and commutativity to check an answer.
• Write and solve an equation with an unknown value.

Success criteria

• I can line up digits by place value before calculating.
• I can regroup accurately and explain what I regrouped.
• I can check addition with a related subtraction or by changing the order of the addends.
• I can solve for an unknown and show how I know it is correct.

Curriculum links

• Number and Operations in Base Ten — place-value relationships in multi-digit numbers.
• Number and Operations in Base Ten — multiplication and division connections that support inverse-operation reasoning.
• Operations and Algebraic Thinking — using parentheses and evaluating numerical expressions.
• Operations and Algebraic Thinking — writing and interpreting expressions that record calculations.

Lesson structure (45 minutes)

1. 0–5 min · Hook and retrieval. Open with the introduction and retrieval slides and display 48,306 + 7,925 without solving. Ask, “What might go wrong if the digits are not aligned?” The student explains the importance of place value and completes a quick mental check: 600 − 275.

2. 5–13 min · Direct teach: addition. Use the place-value modeling slides to model 48,306 + 7,925 in a place-value chart, aligning ones through ten-thousands and regrouping when needed. The student copies the setup, identifies each regrouped unit, and explains why 10 ones equal 1 ten.

3. 13–21 min · Direct teach: subtraction and checking. Continue with the subtraction and checking slides to model 62,004 − 18,769, emphasizing zeros and regrouping across places. The student solves alongside the teacher, then checks by adding the difference to the subtrahend and discusses whether the result is reasonable.

4. 21–33 min · Guided practice. Distribute the aligned-columns practice worksheet and complete the first two problems together: 307,458 + 86,927 and 500,000 − 276,845. Prompt the student to estimate before calculating, align digits, label regrouping, and use an inverse operation to check. The student completes the next problems independently while explaining each decision aloud.

5. 33–40 min · Unknown-value equation. Display the equation from the equation reasoning slides: 36 + 17 + 5 + n = 64. Model combining known addends, then solving for n using subtraction. The student records an equivalent equation, finds n, and substitutes it back to verify the total. Connect the strategy to addition’s commutative property by rearranging the known addends.

6. 40–45 min · Exit check and reflection. Finish with the question stems exit ticket slips. The student selects a slip and responds briefly, then completes the teacher’s exit problems: 73,205 + 18,796 and 90,000 − 47,638. The student must show aligned work, estimate one answer, and solve 24 + 16 + n = 55.

Resources

• the whole-number operations slide deck
• the aligned-columns practice worksheet
• the question stems exit ticket slips
• Place-value chart or whiteboard
• Base-ten blocks or place-value disks
• Pencil, graph paper, and highlighter
• Calculator for teacher verification only

Assessment

• During modeling, ask the student to explain why each digit belongs in its column and what happens when regrouping crosses a zero.
• Check the worksheet for alignment, accurate regrouping, estimation, and use of an inverse operation. Confer immediately when an error appears.
• Use the exit check to identify whether the student can independently add, subtract, check, and solve for an unknown.

Differentiation

• Support with a color-coded place-value chart, graph paper, pre-drawn columns, and sentence starters such as “I regrouped ___ ones as ___ ten” and “I checked by ___.”
• Use place-value disks or base-ten blocks to make regrouping visible, especially for subtraction across zeros.
• If the student needs reduced cognitive load, provide one operation at a time and allow oral explanation before written work.
• For additional challenge, ask the student to create a different equation with the same unknown value and explain how commutativity makes checking easier.